All existing PSOs were exempted from APD in the last change to the UK APD rules - if you refer to the HMRC document, the exclusion is contained towards the back. As a new PSO - i.e. not extant at the date of the exemption coming into force - specific provision would have to be made for a Newquay-London PSO to be exempt from APD, assuming that it's operated by an aircraft on which passengers would normally have to pay it (which is likely).